How competition leads to lumpy or uniform species distributions

A central model in theoretical ecology considers the competition of a range of species for a broad spectrum of resources. Recent studies have shown that essentially two different outcomes are possible. Either the species surviving competition are more or less uniformly distributed over the resource spectrum, or their distribution is 'lumped', consisting of clusters of species with similar resource use that are separated by gaps in resource space. Which of these outcomes will occur crucially depends on the 'competition kernel', which reflects the shape of the resource utilization pattern of the competing species. Most models considered in the literature assume a Gaussian (bell-shaped) competition kernel. This is unfortunate, since predictions based on such a Gaussian assumption are not robust. In fact, Gaussian kernels are a border case scenario of ecologically relevant kernels, and slight deviations from the Gaussian assumption can lead to either uniform or lumped species distributions. Here we illustrate the non-robustness of the Gaussian assumption by simulations of the standard competition model with constant carrying capacity and different competition kernels. In this scenario, lumped species distributions can come about by details of the numerical implementation of the model or by secondary ecological or evolutionary mechanisms.